Police were called to Foot Bridge, on Lock Lane, Castleford, to reports of the injured swan, on Tuesday, March 5.
The swan was taken to the Yorkshire Swan Rescue Hospital, in Selby, where it is recovering from its injuries.
Anyone with any information on the incident is asked to contact West Yorkshire Police on 101, quoting reference number 13190019994.
Information can also be given in complete anonymity to charity CrimeStoppers on 0800 555 111.